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Overview of CFD lattice and its generation method

lattice is the geometric expression of CFD model, and it is also the carrier of simulation and analysis. The lattice quality has an important influence on the computational accuracy and efficiency of CFD. For complex CFD problems, lattice generation is extremely time-consuming and error prone, and the time required to generate lattice is often greater than the time of actual CFD calculation. Therefore, it is necessary to pay enough attention to the lattice generation

1 lattice type

lattice is divided into structural lattice and unstructured lattice. Structural lattice means that the nodes in the lattice are arranged orderly and the relationship between adjacent points is clear, as shown in Figure 1. For a complex region, the structural lattice is constructed in blocks, which forms block structured grids. Figure 2 is an example of a block structure lattice

Figure 1 Structural lattice example

Figure 2 Structural lattice example

different from structural lattice, in unstructured grid, the location of nodes cannot be named orderly with a fixed rule. Figure 3 is an example of an unstructured lattice. Although the generation process of this kind of lattice is relatively complex, it has excellent adaptability, especially for the flow field calculation problems with complex boundaries. Unstructured lattices are usually generated by special programs or software

Figure 3 examples of lattices made of copper plastic plates for non structural doors and windows, furniture, Kitchenware and other purposes

2 classification of lattice units

cells are the basic elements of lattices. In structural lattices, the commonly used ZD lattice elements are quadrilateral elements and 3D lattice elements are hexahedral elements. In unstructured lattices, the commonly used 2D lattice elements are also triangular elements, 3D lattice elements are tetrahedral elements and pentahedral elements, among which the pentahedral elements can also be divided into pyramid (or wedge) and pyramid elements. Fig. 4 and Fig. 5 show commonly used 2D and 3D lattice elements, respectively

commonly used 2D lattice cells in Figure 4

commonly used 3D lattice cells in Figure 5

3 single connected domain and multi connected domain lattice

cell zones are divided into single connected domain and multi connected domain. The so-called single connected domain refers to the case that the boundary line of the solution region does not contain non solution regions. Any closed curve in a simple continuous domain can continuously shrink to a point without crossing its boundary. If there is a non solution region in the solution region, the solution region is called a multi connected region. All flows around are typical multi connected domain problems, such as the flow around wings, the flow around a single blade or a group of blades in a hydraulic turbine or pump, etc. Figures 2 and 3 are examples of multi connected domains

there are two kinds of lattices in the multi connected domain of the flow around problem: O-type and C-type. The O-shaped lattice is like a deformed circle, surrounding the airfoil circle by circle, and the flow conditions can be obtained on the outermost lattice, as shown in Figure 6. The C-shaped lattice is like a deformed C-shaped, surrounding the outside of the airfoil, as shown in Figure 7. These two lattices belong to structural lattices

Figure 6 O-shaped lattice

Figure 7 C-shaped lattice

4 lattice generation process

whether it is structural lattice or unstructured lattice, it is necessary to generate lattice according to the following process:

(1) both geometric models are established. Geometric model is the carrier of lattice and boundary. For two-dimensional problems, the geometric model is a two-dimensional surface; For three-dimensional problems, the geometric model is a three-dimensional solid

(2) dividing grid. In the generated geometric model soil, the specific lattice type, lattice element and lattice density are applied to divide the face or body to obtain the lattice

(3) specify boundary recognition. Specify the name and type of each area of the model to prepare for the physical properties, boundary conditions and initial conditions of the subsequent given model

the key to generating lattice is the step (2) in the above process. Because the traditional CFD is based on structural lattices, there are many mature generation technologies for structural lattices, while the generation technology for unstructured lattices is more complex

5 body fitted coordinate method for generating structural lattices

if the boundaries of the calculation region are a regular region parallel to the coordinate axis, the region can be easily divided and a uniform lattice can be generated quickly. However, the boundary of practical engineering problems cannot exactly match with various coordinate systems. Therefore, it is necessary to construct a coordinate system with mathematical methods, and its coordinate axes exactly match the boundary of the calculated object. This coordinate system is called body fitted coordinates. Rectangular coordinate system is the body fitted coordinate system of rectangular area, and polar coordinate system is the body fitted coordinate system of circular sector area

the basic idea of generating lattices using body fitted coordinate system can be described as follows

(a) X-Y physical plane (b) ξ-η Calculation plane

figure 8 body fitted coordinate schematic diagram

it is assumed that there is an irregular region in the X-Y few plane shown in Figure 8 (a). Now, in order to construct a body fitted coordinate system suitable for this region, the two boundaries intersecting in this region are taken as the two axes of the curvilinear coordinate system, and are recorded as ξ and η。 On the four sides of the object, different locations can be specified ξ and η Value. For example, we can assume that there is a ξ= 0 η= 0, and there is at point C ξ= 1， η= 1。 In this way, you can ξ-η As two axes of rectangular coordinate system on another calculation plane, according to the above specified ξ and η The solution area on the calculation plane is simplified into a rectangular area. As long as the total number of nodes in each direction is given, a uniformly distributed lattice can be generated immediately, as shown in Figure 8 (b). Now, if we can find the relation between ξ-η At the corresponding position of any point on the plane, the lattice on the physical plane can be easily generated. Therefore, the remaining problem is how to establish the relationship between the two planes, which is the method of generating body fitted coordinates. The commonly used methods of generating body fitted coordinates include algebraic method and differential equation method

the so-called algebraic method is to convert the irregular region on the physical plane into the rectangular region on the computational plane through some algebraic relations. There are many kinds of algebraic methods, including boundary gauge method, double boundary method and infinite interpolation method. The differential equation method is to convert the physical plane into the computational plane through a differential equation. The essence of this method is the solution to the boundary value problem of differential equations: when installing the electronic universal tensile machine, 1 it must be installed and solved according to the steps and methods in the manual of Jinan wance electronic tensile machine. This method is a very effective method to construct body fitted coordinates, and it is also widely used by most lattice generation software. In this method, elliptic, hyperbolic and parabolic partial differential equations can be used to generate lattices, among which elliptic equations are more used. For detailed information about algebraic method and differential equation method, please refer to relevant literature

6 generating this project will include the special software for adding satellite function grids in LEGO factories all over the world. Grid generation is a "long and boring" work process, which often requires a lot of experiments to succeed. Therefore, there are many commercialized professional lattice generation software. Such as gambit, TGrid, geomesh, prebfc and ICEM CFD. In addition, some CFD or finite element substructure analysis software, such as ANSYS, I-DEAS, NASTRAN, Patran and Aries, also provide professional lattice generation tools

the use methods of these software or tools are similar, and the generated grid files can often be shared among the software. For example, fluent can read the grids generated by the above software

it should be noted that because lattice generation involves geometric modeling, especially 3D solid modeling, many lattice generation software, in addition to providing geometric modeling functions, also allow users to use CAD software (such as AutoCAD, pro/engineer) to generate geometric models for more than 50 years, and then import them into lattice software for lattice division. Therefore, the use of pre-processing software often involves the manufacturing function of CAD software. (end)

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